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The Journal of Chemical Physics

Hyperfine structure effects in probing atomic alignment

I. M. Bell, C. J. K. Quayle, Keith R. Burnett

Published Feb 1, 1995• 1 citation
Publisher

Abstract

We have performed an analysis of the effect of hyperfine structure in an experiment in which an aligned excited state is probed using linearly polarized light. The state is born with a given electronic alignment resulting from a collisional process. It is probed after a time which is short in comparison to its radiative lifetime but much longer than ω−1hfs, where ℏωhfs is the hyperfine splitting. This means that hyperfine structure has ample time to ‘‘develop.’’ It is therefore essential to take into account both the hyperfine structure of the level and the manner in which the alignment is affected by recoupling to the new basis. Ratios of fluorescent intensities for different laser polarization configurations contain information on the alignment of the system. We show how these may be calculated for a system with several isotopes, some of which have hyperfine structure, and where many components are probed with appreciable strength. A comparison is made with our experimental results for the Hg(6 3P1) level probed on the 6 3P1–7 3S1 transition. The presence of hyperfine structure has a considerable influence on the measurements. It is important to understand such effects if one is to obtain information on the nascent electronic alignment by observation of the fluorescent intensities.

DOI
10.1063/1.468754

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We have performed an analysis of the effect of hyperfine structure in an experiment in which an aligned excited state is probed using linearly polarized light. The state is born with a given electronic alignment resulting from a collisional process. It is probed after a time which is short in comparison to its radiative lifetime but much longer than ω−1hfs, where ℏωhfs is the hyperfine splitting. This means that hyperfine structure has ample time to ‘‘develop.’’ It is therefore essential to take into account both the hyperfine structure of the level and the manner in which the alignment is affected by recoupling to the new basis. Ratios of fluorescent intensities for different laser polarization configurations contain information on the alignment of the system. We show how these may be calculated for a system with several isotopes, some of which have hyperfine structure, and where many components are probed with appreciable strength. A comparison is made with our experimental results for the Hg(6 3P1) level probed on the 6 3P1–7 3S1 transition. The presence of hyperfine structure has a considerable influence on the measurements. It is important to understand such effects if one is to obtain information on the nascent electronic alignment by observation of the fluorescent intensities.
Coefficients are calculated for the alignment transfer between levels of hyperfine structure (hfs) of atoms with electron momenta j=1, 1.5, and 2 and nuclear spins i=0.5, 1, 1.5, 2, 2.5, 3, and 3.5 under the influence of nonresonance collisions with atoms of a foreign gas. The results are tabulated. A concrete application of the results is illustrated in calculating numerical values of the effective cross sections for collisional transfer of alignment between hfs levels of the first excited nsup2sup 2sup2Psub3sub 3sub3/sub2sub 2sub2 state of rubidium and cesium atoms. (AIP)
The possibility of probing the collisions of aligned Rydberg atoms by stimulated emission is assessed with studies of a polarized state and a new measurement of a collisional alignment effect in atomic Ca. The stimulated emission method uses a laser to dump the desired state to a lower level which subsequently fluoresces. The technique can be used to obtain populations and polarization dependent information. First, the method is tested by applying it to an aligned Ca(4s17d 1D2) state. Alignment curves are measured when the initial state is prepared with both parallel and perpendicular relative polarizations. The experimentally observed alignment compares well with that derived from theoretical considerations of a saturated stimulated transition. Second, a two-vector collisional alignment experiment (initial state and relative velocity vector) is performed to study the energy transfer process Ca(4s7d 1D2)+He→Ca(4s6f 1F3)+He+ΔE=17.7 cm−1, and alignment effects are measured by both stimulated emission and conventional direct fluorescence detection. A preference for the ‖m‖=1 and 2 initial states is observed in the relative cross sections. Essentially identical data are obtained with the two detection methods when elliptically polarized light is used for the stimulated emission detection method. The stimulated emission technique can provide alignment and population information of the final states, making it an excellent new tool for both three-vector correlation experiments and state-to-state Rydberg transitions.
Breit has derived formulae giving the polarization P(H)P(H)P(H) and the angle of maximum polarization $\ensuremath{\theta}$ of a resonance line showing hyperfine structure, as a function of a weak magnetic field applied in the direction of observation of the resonance radiation. The formulae give a means of estimating the effect of hyperfine structure on the calculation of the mean life $\ensuremath{\tau}$ of an excited atom from experiments on the magnetic depolarization and rotation of the plane of polarization of resonance radiation. The calculation has been carried through for the case of the resonance line of $\mathrm{Cd}(\ensuremath{\lambda}3261)$ and that of $\mathrm{Hg}(\ensuremath{\lambda}2537)$, and it is found that the differences between the value of $\ensuremath{\tau}$ calculated from hyperfine structure data and that calculated from $tan2\ensuremath{\theta}$ by the usual non-hyperfine structure method lie well within the experimental error. P(H)P0\frac{P(H)}{{P}_{0}}P0​P(H)​ is found to be practically the same whether hyperfine structure is taken into account or neglected. This is due to the fact that the greatest contribution of the polarization in these cases comes from the isotopes having no nuclear spin and the ggg-value for the upper state of these isotopes is larger than any other upper hyperfine structure state involved. The mean lives of the 73S17^{3}S_{1}73S1​ state of mercury have been recalculated from Richter's data on the polarization of stepwise radiation. The values of $\ensuremath{\tau}$ obtained by this method of calculation are 7.2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}9}$ for $\ensuremath{\lambda}4047$, 1.69\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$ for $\ensuremath{\lambda}4358$ and 1.53\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$ for $\ensuremath{\lambda}5461$. A discussion of Richter's results is given.
We have measured the alignment of the photofragments produced by photodissociation of Hg–Ar van der Waals molecules using light around 253.7 nm. The molecules are produced in the X0+ ground state in a supersonic expansion. Tunable laser light close to the Hg 6 1S0–6 3P1 transition is then used to excite the molecule to the B1± state, in which it dissociates. The alignment of the resulting Hg(3P1) asymptotic atoms is probed by tuning a delayed second laser to the 435.8 nm Hg 6 3P1–7 3S1 atomic transition and monitoring the subsequent fluorescence on the 7 3S1–6 3P2 transition around 546.1 nm. These measurements have been made, we believe for the first time, as a function of dissociating energy from very close to threshold to higher energies. The alignment shows a significant rise with increasing photon energy in line with a semiclassical picture of orbital locking at lower energies and rapid decoupling at higher energies. The results exhibit good agreement with the results of a fully quantum mechanical theory of the system.
We have measured the alignment of Hg(6 3^{3}3P1{\mathit{P}}_{1}P1​) atoms following off-resonant excitation of the Hg 6 1S0^{1}\mathrm{S}_{0}1S0​--6 3P1^{3}\mathrm{P}_{1}3P1​ transition in the presence of Kr. We present a polarization spectrum for both red and blue wings out to detunings beyond 100 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. This represents a considerable extension to the existing results, which has been made possible by the use of a pump-and-probe excitation scheme. In the experiment a pulsed laser, detuned from the resonance, creates an alignment in the upper state. This is probed by tuning a delayed second laser to a higher transition and monitoring laser-induced fluorescence from the two-step process. The alignment of the asymptotic Hg(6 3^{3}3P1{\mathit{P}}_{1}P1​) atoms is determined by comparison of the signals obtained for different relative polarizations of the lasers. We discuss the advantages of this method and the relation of the raw data to the polarizations presented. The results are discussed within the context of a simple quasiclassical model of the process.
In the optical excitation of atoms with polarized light, producing excited atoms, only some of the Zeeman sublevels of the excited state are actually reached, so that large differences of population can be built up between Zeeman sublevels or between hyperfine structure (hfs) levels. This property can be used to detect radio-frequency resonance in optically excited atomic states. These resonances produce a characteristic change in intensity or in the degree of polarization of the light re-emitted. Zeeman intervals, Stark effects, and hfs intervals can be measured in this manner. (The Stark constant of the 63P1 level of Hg and the electric quadrupole moments of the alkali atoms have been obtained in this way.)The technique of “optical pumping” gives a way to concentrate atoms in some of the Zeeman sublevels of one of the hfs levels of the ground state.Atomic orientation has been obtained with the Na atom, in an atomic beam and in the vapor in equilibrium with the metal. The orientation effects have been studied by detection of radio-frequency resonance signals in the ground state. Orientation can be increased many times by adding a variable pressure of a foreign gas to the pure Na vapor. Because of the coupling between nuclear spin and electron spin, nuclear orientation is produced at the same time as atomic orientation.